Performance Level Descriptors Algebra I

Performance Level Descriptors – Algebra I

Revised October 28, 2015 of 10

Algebra I: Sub-Claim A The student solves problems involving the Major Content for the grade/course with connections to the Standards for

Mathematical Practice.

Level 5: Exceeds Expectations Level 4: Meets Expectations Level 3: Approaches

Expectations Level 2: Partially Meets

Expectations

Expressions

A-SSE.1-1

A-SSE.1-2

A-SSE.2-1

A-SSE.2-4

A.APR.1-1

Writes and analyzes equivalent numerical and polynomial expressions in one variable, using addition, subtraction, multiplication and factoring, including multi-step problems. Interprets parts of complicated exponential and quadratic expressions that represent a quantity in terms of its context.

Writes equivalent numerical and polynomial expressions in one variable, using addition, subtraction, multiplication and factoring. Interprets parts of exponential and quadratic expressions that represent a quantity in terms of its context.

Writes equivalent numerical and polynomial expressions in one variable, using addition, subtraction and multiplication. Identifies components of exponential and quadratic expressions.

Writes equivalent numerical and polynomial expressions in one variable, using addition, subtraction and multiplication. Identifies components of exponential expressions.

Interpreting Functions

F-IF.1

F-IF.2

F-IF.A.Int.1

F-IF.4-1 F-IF.5-1 F-IF.5-2

Determines if a given relation is

a function.

Evaluates with, uses and

interprets with function

notation within a context.

Given a context, writes and analyzes a linear or quadratic function.

For linear and quadratic

functions that model contextual

relationships, determines and

interprets key features, graphs

the function and solves

problems. Determines the domain and relates it to the quantitative


a function.

Evaluates with and uses

function notation within a

context.

Given a context, writes a linear function.

For linear and quadratic


relationships, determines key

features and graphs the

function.

Determines the domain and relates it to the quantitative


a function.


function notation.

Given a context, writes a linear function. For linear and quadratic



features. Determines the domain of linear and quadratic functions.

Determines if a given relation is a function. Evaluates with and uses function notation. Given a context, writes a linear function. Given the graph of linear



features.







Expectations

relationship it describes for a linear, quadratic, exponential (limited to domains in the integers), square root, cube root, piece-wise, step and absolute value functions.

relationship it describes for linear, quadratic and exponential (limited to domains in the integers) functions.

Rate of Change

F-IF.6-1a

F-IF.6-1b

F-IF.6-6a F-IF.6-6b

Calculates and interprets the average rate of change of linear, exponential, quadratic, square root, cube root and piecewise-defined functions (presented symbolically or as a table) over a specified interval, and estimates the rate of change from a graph. Compares rates of change associated with different intervals.

Calculates the average rate of change of linear, exponential and quadratic functions (presented symbolically or as a table) over a specified interval and estimate the rate of change from a graph.

Calculates the average rate of change of linear, exponential and quadratic functions (presented symbolically or as a table) over a specified interval.

Calculates the average rate of change of linear, exponential and quadratic functions (presented symbolically or as a table) over a specified interval.

Solving Algebraically

A-REI.3

A-REI.4a-1

A-REI.4b-1 A.REI.4b-2

A-CED.4-1

A-CED.4-2

HS-Int.1

HS-Int.2

HS-Int.3-2

Algebraically solves linear

equations, linear inequalities

and quadratics in one variable

(at complexity appropriate to

the course), including those

with coefficients represented

by letters.

Utilizes structure and rewriting

as strategies for solving.

Algebraically solves linear equations, linear inequalities and quadratics in one variable (at complexity appropriate to the course), including those with coefficients represented by letters.

Algebraically solves linear equations, linear inequalities and quadratics in one variable (at complexity appropriate to the course).

Algebraically solves linear equations and linear inequalities in one variable (at complexity appropriate to the course).







Expectations

Solving Graphically

A-CED.3-1

A-REI.10

A-REI.11-1a

A-REI.11-1b

A-REI.12

Graphs and analyzes the

solution sets of equations,

linear inequalities and

systems of linear inequalities.

Finds the solutions to two

polynomial functions

approximately, e.g., using

technology to graph the

functions, make tables of

values, or find successive

approximations.

Writes a system of linear

inequalities given a context.

Graphs the solution sets of


and systems of linear

equations and linear

inequalities.

Finds the solutions to two polynomial functions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.



inequalities. Finds the solutions to two polynomial functions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.

Graphs the solution sets of equations and linear inequalities.

Given the graph, identify the solutions of a system of two polynomial functions.



Algebra I: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with connections to the

Standards for Mathematical Practice.



Expectations

Number Systems

N-RN.B-1

Identifies rational and

irrational numbers.

Calculates sums and

products of two rational

and/or irrational numbers

and determines whether

and generalizes when the

sums and products are

rational or irrational.


irrational numbers.

Calculates sums and

products of two rational

and/or irrational numbers.


irrational numbers. Identifies rational and

irrational numbers.

Equivalent Expressions and Functions

A-SSE.3a

A-SSE.3b

A-SSE.3c-1 F.IF.8a

Determines equivalent forms

of quadratic and exponential

(with integer domain)

expressions and functions to

reveal and explain their

properties.

Determines equivalent forms

of quadratic expressions and

functions.

Uses equivalent forms

to reveal and explain

zeros, extreme values

and symmetry.

Identifies equivalent forms of

quadratic expressions and

functions.

Identifies zeros and

symmetry.

Identifies equivalent forms of

quadratic expressions and

functions in cases where

suitable factorizations are

provided.

Interpreting Graphs of Functions A-APR.3-1 F-IF.7a-1 F-IF.7a-2 F-IF.7b

Graphs linear, quadratic,

cubic (in which linear and

quadratic factors are

available), square root, cube

root and piecewise-defined

functions, showing key

features.

Determines a function, given a

graph with key features

identified.

Graphs linear, quadratic and

cubic (in which linear and

quadratic factors are

available) functions, showing

key features.

Graphs linear and quadratic


features.

Graphs linear functions,

showing key features.







Expectations

Function Transformations

F-BF.3-1 F-BF.3-4

Identifies the effects of

multiple transformations on

graphs of linear and quadratic

functions and finds the value

of k given a transformed

graph.

Experiments with cases using

technology. Given the equation of a

transformed linear or

quadratic function, creates

an appropriate graph.

Identifies the effects of a

single transformation on


functions, including f(x)+k,

kf(x), f(kx) and f(x+k), and

finds the value of k given a

transformed graph.




functions, limited to f(x)+k

and kf(x).

Identifies the effects of a single

transformation on graphs of

linear and quadratic functions,

limited to f(x)+k.

Multiple Representations of Functions A-REI.6-1 F-LE.2-1 F-LE.2-2

F-IF.9-1

F-Int.1-1

S-ID.Int.1

S-ID.Int.2

HS-Int.1

HS-Int.2

HS-Int.3-1

HS-Int.3-2

Writes and analyzes systems

of linear equations in multi-

step contextual problems.

Represents linear and exponential (with domain in the integers) functions symbolically, in real-life scenarios, graphically, with a verbal description, as a sequence and with input- output pairs to solve mathematical and contextual problems. Compares the properties of

two functions represented in

multiple ways, limited to

linear, exponential (with

domains in the integers),

Writes systems of linear

equations in multi-step

contextual problems.

Represents linear and

exponential (with domain in

the integers) functions

symbolically, graphically and

with input-output pairs to

solve mathematical problems. Compares the properties of


different ways, limited to

linear quadratic, and,

Writes systems of linear

equations in multi-step


Given a symbolic representation, real‐life scenario, graph, verbal description, sequence or input-output pairs for linear and exponential functions (with domains in the integers), solves mathematical problems. Compares the properties of


different ways, limited to

linear and quadratic.

Writes systems of linear equations in simple contextual problems. Given a symbolic representation, real‐life scenario, graph, verbal description, sequence or input-output pairs for linear functions, solves mathematical problems. Compares the properties of

two linear functions

represented in different ways.







Expectations

quadratic, square root and,

absolute value cube root,

piecewise and step.

exponential (with domains in

the integers).

Summarizing Representing and Interpreting Data

S-ID.5

S-ID.Int.1 S-ID.Int.2

Determines appropriate

representations of categorical

and quantitative data,

summarizing and interpreting

the data and characteristics of

the representations.

Describes and interprets

possible associations and

trends in the data.

Determines appropriate

representations of categorical

and quantitative data,

summarizing the data and

characteristics of the

representations.

Given representations of

categorical and quantitative

data, summarizes the data

and characteristics of the

representations.

Given representations of categorical and quantitative data, describes the characteristics of the representations.



Algebra I: Sub-Claim C In connection with content, the student expresses course-level appropriate mathematical reasoning by constructing viable arguments,

critiquing the reasoning of others and/or attending to precision when making mathematical statements.



Expectations

Reasoning

HS.C.2.1

HS.C.5.5

HS.C.5.6

HS.C.5.10.1

HS.C.6.1

HS.C.8.1

HS.C.9.1

HS.C.10.1

HS.C.12.1

HS.C.16.2

HS.C.18.1

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student clearly constructs and communicates a complete response based on:

the principle that a graph of an equation in two variables is the set of all its solutions

reasoning about linear and exponential growth

properties of rational numbers or irrational numbers

transformations of functions

a chain of reasoning to justify or refute algebraic, function, or linear-equation propositions or conjectures

a given equation or system of equations

the number or nature of solutions by:

using a logical approach based

on a conjecture and/or stated

assumptions, utilizing

mathematical connections

(when appropriate)providing an

efficient and logical progression

of steps or chain of reasoning

with appropriate justification

performing precise calculations

using correct grade-level

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student clearly constructs and communicates a response based on:



properties of rational numbers of rational numbers or irrational numbers





using a logical approach based on

a conjecture and/or stated



(when appropriate)

providing a logical progression of

steps or chain of reasoning with

appropriate justification performing precise calculations

using correct grade-level

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student constructs and communicates a partial response based on:










assumptions

providing a logical, but

incomplete, progression of

steps or chain of reasoning

performing minor calculation errors

using some grade-level

vocabulary, symbols and labels

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student constructs and communicates an incomplete response based on:





a chain of reasoning to justify or refute algebraic, function or linear-equation propositions or conjectures



using an approach based on a

conjecture and/or stated or

faulty assumptions

providing an incomplete or

illogical progression of steps or

chain of reasoning

making an intrusive calculation

error

using limited grade-level




Algebra I: Sub-Claim C In connection with content, the student expresses course-level appropriate mathematical reasoning by constructing viable arguments,




Expectations vocabulary, symbols and labels

providing a justification of a

conclusion

determining whether an

argument or conclusion is

generalizable

evaluating, interpreting and

critiquing the validity of others’

responses, approaches and

reasoning – utilizing


(when appropriate) – and

providing a counter-example

where applicable


providing a justification of a conclusion

evaluating, interpreting and critiquing the validity of others’ responses, approaches and reasoning - utilizing mathematical connections (when appropriate)

providing a partial justification

of a conclusion based on own

calculations

evaluating the validity of

others’ approaches and

conclusions

providing a partial justification

of a conclusion based on own

calculations



Algebra I: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by

applying knowledge and skills articulated in the standards for the current grade/course (or for more complex problems, knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling practice, and where

helpful making sense of problems and persevering to solve them, reasoning abstractly, and quantitatively, using appropriate tools strategically, looking for the making use of structure and/or looking for and expressing regularity in repeated reasoning.



Expectations

Modeling

HS.D.1-1 HS.D.2-5 HS.D.2-6 HS.D.2-8 HS.D.2-9 HS.D.3-1a HS.D.3-3a

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student devises and enacts a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by: using state assumptions and making

assumption and approximations to simplify a real-world situation (includes micro‐models)

mapping relationships between important quantities

selecting appropriate tools to create models

analyzing relationships mathematically between important quantities to draw conclusion

analyzing and/or creating constraints, relationships and goals

interpreting mathematical results in the context of the situation

reflecting on whether the results make

sense

improving the model if it has not served its purpose

writing a complete, clear and correct algebraic expression or equation to describe a situation

applying proportional reasoning and percentages justifying and defending

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student devises and enacts a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by:

using stated assumptions and making assumptions and approximations to simplify a real-world situation(include micro-models)


selecting appropriate tools to create models

analyzing relationships

mathematically between

important quantities to

draw conclusions


reflecting on whether the results make sense


writing a complete, clear

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student devises and enacts a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by:

using state assumptions and approximations to simplify a real-world situation

illustrating relationships between important quantities

using provided tools to create models

analyzing relationship mathematically between important quantities to draw conclusions

interpreting mathematical

results in a simplified

context


modifying the model if it has not served its purpose

writing an algebraic expression or equation to

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student devises a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by:

using stated assumptions and approximations to simplify a real-world situation

identifying important quantities

using provided tools to create models

analyzing relationships mathematically to draw conclusions

writing an algebraic expression or equation to describe a situation

applying proportional reasoning and percentages

using functions to describe how one quantity of interest depends on another

using statistics using estimates of known



Algebra I: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by





Expectations

models which lead to a conclusion using functions in any form to describe

how one quantity of interest depends on another

using statistics using reasonable estimates of known

quantities in a chain of reasoning that yields an estimate of an unknown quantity

and correct algebraic expression or equation to describe a situation

applying proportional reasoning and percentages

writing and using functions in any form to describe how one quantity of interest depends on another

using statistics

using reasonable estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity

describe a situation applying proportional

reasoning and percentages writing and using functions

to describe how one quantity of interest depends on another

using statistics using reasonable estimates

of known quantities in a chain of reasoning that yields an estimate of an unknown quantity


Performance Level Descriptors – Geometry

Revised October 28, 2015 Page 1 of 8

Geometry: Sub-Claim A The student solves problems involving the Major Content for the grade/course with connections to the




Expectations

Congruence Transformations

G-CO.6 G-CO.C

Determines and uses

appropriate geometric

theorems and properties of

rigid motions, lines, angles,

triangles and parallelograms to

solve problems and prove

statements about angle

measurement, triangles,

distance, line properties and

congruence.

Uses given geometric theorems

and properties of rigid motions,

lines, angles, triangles and

parallelograms to solve routine

problems and prove




congruence.

Uses given geometric




solve routine problems and

reason about angle



congruence.





solve routine problems.

Similarity

G-SRT.1a

G-SRT.1b

G-SRT.2

G-SRT.5

Uses transformations and

congruence and similarity

criteria for triangles to prove

relationships among geometric

figures and to solve problems.

Uses transformations to

determine relationships among

simple geometric figures and

to solve problems.

Identifies transformation

relationships in simple

geometric figures.

Identifies transformation

relationships in simple

geometric figures in cases

where an image is provided.

Similarity in Trigonometry

G-SRT.6

G-SRT.7-2

G-SRT.8

Uses trigonometric ratios, the

Pythagorean Theorem and the

relationship between sine and

cosine to solve right triangles

in applied problems.

Uses similarity transformations

with right triangles to define

trigonometric ratios for acute

angles.






Uses trigonometric ratios and

the Pythagorean Theorem to

determine the unknown side

lengths and angle

measurements of a right

triangle.

Uses trigonometric ratios and

the Pythagorean Theorem to

determine the unknown side

lengths of a right triangle.



Geometry: Sub-Claim A The student solves problems involving the Major Content for the grade/course with connections to the




Expectations

Modeling and Applying

G-SRT.7-2 G-SRT.8 G-GPE.6 G-Int.1

Uses geometric relationships

in the coordinate plane to

solve problems involving

area, perimeter and ratios of

lengths.

Applies geometric concepts and

trigonometric ratios to

describe, model and solve

applied problems (including

design problems) related to the

Pythagorean Theorem, density,

geometric shapes, their

measures and properties.





lengths.

Applies geometric concepts to


applied problems related to the

Pythagorean Theorem,



Uses provided geometric

relationships in the coordinate

plane to solve problems

involving area and perimeter.



applied problems related to

the Pythagorean Theorem,



Uses provided geometric relationships in the coordinate plane to solve problems involving area and perimeter. Applies geometric concepts to




measures, and properties.



Geometry: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with connections to the




Expectations

Transformations

G-CO.1 G-CO.3 G-CO.5

Given a figure and a sequence of transformations, draws the transformed figure.

Uses precise geometric terminology to specify a sequence of transformations that will carry a figure onto itself or another.

Given a figure and a transformation, draws the transformed figure. Specifies a sequence of transformations that will carry a figure onto another.

Given a figure and a transformation, draws the transformed figure.

Given a figure and a transformation, identifies a transformed figure.

Geometric Constructions

G-CO.D

Understands geometric

constructions: copying a

segment, copying an angle,

bisecting an angle, bisecting a

segment, including the

perpendicular bisector of a line

segment.

Given a line and a point not on

the line, uses a variety of tools

and methods to construct

perpendicular and parallel

lines.

Uses a variety of tools and

methods to construct

equilateral triangles, squares,

and hexagons inscribed in

circles.

Understands geometric

constructions: copying a

segment, copying an angle,

bisecting an angle, bisecting a

segment, including the

perpendicular bisector of a line

segment.

Given a line and a point not on the line, constructs perpendicular and parallel lines.

Understands basic geometric constructions: copying a segment, copying an angle, bisecting an angle, bisecting a segment, including the perpendicular bisector of a line segment.

Understands basic geometric constructions: copying a segment, and copying an angle.



Geometry: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with connections to the




Expectations

Applying Geometric Properties and Theorems

G-C.2

G-C.B

G-GPE.1-1 G-GPE.1-2

Applies properties and

theorems of angles, segments

and arcs in circles to solve

problems and model

relationships.

Completes the square to find

the center and radius of a

circle given by an equation.




problems.




Applies properties and theorems of angles, segments and arcs in circles to solve problems.

Applies properties and theorems of angles and segments to solve problems.

Geometric Formulas G-GMD.1 G-GMD.3 G-GMD.4

Uses volume formulas to solve mathematical and contextual problems that involve cylinders, pyramids, cones and spheres. Uses dissection arguments, Cavalieri’s principle and informal limit arguments to support the formula for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

Identifies the shapes of two-dimensional cross-sections of three-dimensional objects

and identifies three-

dimensional objects

generated by rotations of

two-dimensional objects.

Using formulas, determines the volume of cylinders, pyramids, cones and spheres. Gives an informal argument for the formula for the circumference of a circle and area of a circle, including dissection arguments.

Identifies the shapes of two-

dimensional cross-sections of

three-dimensional objects.

Using formulas, determines the volume of cylinders, pyramids, cones and spheres.

Identifies the shapes of two-dimensional cross-sections of three-dimensional objects,.

Using formulas, determines the volume of cylinders, pyramids, cones and spheres. Identifies the shapes of two-dimensional cross-sections of three-dimensional objects, when cross sections are parallel or perpendicular to a base/face.



Geometry: Sub-Claim C In connection with content, the student expresses course-level appropriate mathematical reasoning by constructing viable arguments,


Level 5: Exceeds Expectations Level 4: Meets Expectations Level 3: Approaches Expectations Level 2: Partially Meets

Expectations

Reasoning HS.C.13.1 HS.C.13.2 HS.C.13.3 HS.C.14.1 HS.C.14.2 HS.C.14.3 HS.C.14.5 HS.C.14.6

HS.C.15.14

HS.C.18.2

In connection with the content

knowledge, skills, and abilities

described in Sub-claims A and B, the

student clearly constructs and

communicates a complete response

based on: • a chain of reasoning to justify or

refute algebraic and/or geometric

propositions or conjectures • geometric reasoning in a

coordinate setting, OR • a response to a multi-step problem, by: • using a logical approach based on a

conjecture and/or stated


mathematical connections (when

appropriate) • providing an efficient and logical

progression of steps or chain of

reasoning with appropriate

justification • performing precise calculation • using correct grade- level

vocabulary, symbols and labels • providing a justification of a

conclusion

• determining whether an

argument or conclusion is

generalizable • evaluating, interpreting and







communicates a response based on: • a chain of reasoning to justify or



coordinate setting, OR • a response to a multi-step

problem, by: • using a logical approach based on




appropriate) • providing a logical progression of

steps or chain of reasoning with

appropriate justification • performing precise calculations • using correct grade-level


conclusion • evaluating, interpreting and



reasoning – utilizing


appropriate).




student constructs and

communicates a partial response

based on: • a chain of reasoning to justify or




problem, by: • using a logical approach based on


assumptions • providing a logical, but

incomplete, progression of steps

or chain of reasoning • performing minor calculation

errors • using some grade-level

vocabulary, symbols and labels • providing a partial justification of

a conclusion based on own calculations

• evaluating the validity of others’ approaches and conclusions




student constructs and communicates

an incomplete response based on: • a chain of reasoning to justify or




problem, by : • using an approach based on a

conjecture and/or stated or faulty

assumptions • providing an incomplete or illogical

chain of reasoning, or progression

of steps • making an intrusive calculation

error • using limited grade-level

vocabulary, symbols and labels • providing a partial justification of a

conclusion based on own

calculations



Geometry: Sub-Claim C In connection with content, the student expresses course-level appropriate mathematical reasoning by constructing viable arguments,



Expectations reasoning – utilizing mathematical

connections (when appropriate) –

and providing a counter example

where applicable.



Geometry: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by applying

knowledge and skills articulated in the standards for the current grade/course (or for more complex problems, knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling practice, and where helpful making sense of problems and persevering to solve them, reasoning abstractly, and quantitatively, using appropriate tools strategically, looking for the

making use of structure and/or looking for and expressing regularity in repeated reasoning.


Expectations

Modeling HS.D.1-2

HS.D.2-1

HS.D.2-2

HS.D.2-11

HS.D.3-2a

HS.D.3-4a



described in Sub-claims A and B,

devises and enacts a plan to apply

mathematics in solving problems

arising in everyday life, society and

the workplace by: • using stated assumptions and

making assumptions and

approximations to simplify a re‐

world situation (includes micro-

models) • mapping relationships between

important quantities

• selecting appropriate tools to

create models • analyzing relationships


important quantities to draw

conclusion

• analyzing and/or creating

constraints, relationships and

goals

• interpreting mathematical results

in the context of the situation

• reflecting on whether the results

make sense

• improving the model if it has not

served its purpose

• writing a complete, clear and








making assumptions and

approximations to simplify a real-

world situation (includes micro-

models) • mapping relationships between

important quantities

• selecting appropriate tools to create models

• analyzing relationships mathematically between important quantities to draw conclusions




make sense • improving the model if it has not

served its purpose


correct algebraic expression or

equation to describe a situation

• applying proportional









world situation

• illustrating relationships between

important quantities • using provided tools to create

models • analyzing relationships



conclusions


in a simplified context


make sense

• modifying the model if it has not

served its purpose

• writing an algebraic expression

or equation to describe a

situation


reasoning and percentages • applying geometric principles




devises a plan to apply





world situation

• identifying important quantities • using provided tools to create

models

• analyzing relationships

mathematically to draw

conclusions • writing an algebraic expression or


• applying proportional reasoning

and percentages

• applying common geometric

principles and theorems

• using functions to describe how

one quantity of interest depends

on another

• using estimates of known

quantities in a chain of reasoning

that yields an estimate of an

unknown quantity



Geometry: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by applying

knowledge and skills articulated in the standards for the current grade/course (or for more complex problems, knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling practice, and where helpful making sense of problems and persevering to solve them, reasoning abstractly, and quantitatively, using appropriate tools strategically, looking for the

making use of structure and/or looking for and expressing regularity in repeated reasoning.


Expectations correct algebraic expression or


• applying proportional reasoning

and percentages justifying and

defending models which lead to a

conclusion

• applying geometric principles and

theorems

• writing and using functions in any

form to describe how one

quantity of interest depends on

another

• using reasonable estimates of

known quantities in a chain of

reasoning that yields an estimate

of an unknown quantity

reasoning and percentages

• applying geometric principles

and theorems

• writing and using functions in any form to describe how one quantity of interest depends on another

• using reasonable estimates of

known quantities in a chain of

reasoning that yields an

estimate of an unknown

quantity

and theorems • writing and using functions to

describe how one quantity of

interest depends on another

• using reasonable estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity

Performance Level Descriptors – Algebra II


Algebra II: Sub-Claim A The student solves problems involving the Major Content for the grade/course with connections to the



Expectations

Level 2: Partially Meets Expectations

Equivalent Expressions

N-RN.2

A.Int.1

A-REI.2

A-SSE.2-3

A-SSE.2-6

A-SSE.3c-2

Uses mathematical properties

and structure of polynomial,

exponential, rational and radical

expressions to create equivalent

expressions that aid in solving

mathematical and contextual

problems.

Rewrites exponential

expressions to reveal quantities

of interest that may be useful.


and structure of polynomial,

exponential and rational

expressions to create

equivalent expressions.

Rewrites exponential

expressions to reveal

quantities of interest that

may be useful.

Uses provided mathematical

properties and structure of

polynomial and exponential




properties and structure of

exponential expressions to

identify equivalent

expressions.


A-APR.2

A-REI.11-2

F-IF.4-2


and relationships to reveal key

features of polynomial,

exponential, rational,

trigonometric and logarithmic

functions, using them to sketch

graphs and identify


relationship between two

quantities, and applying the

remainder theorem where

appropriate.

Interprets key features of

graphs and tables, and uses

mathematical properties and

relationships to reveal key


exponential and rational

functions, using them to sketch

graphs.


properties and relationships

to reveal key features of


functions, using them to

sketch graphs.

Given a graph of a polynomial

or exponential function,

identifies key features.






Expectations


Rate of Change

F-IF.6-2 F-IF.6-7

Calculates and interprets the

average rate of change of

polynomial, exponential,

logarithmic or trigonometric

functions (presented

symbolically or as a table) over

a specified interval, and

estimates the rate of change

from a graph.

Compares rates of change

associated with different

intervals.

Calculates the average rate of

change of polynomial and

exponential functions

(presented symbolically or as a

table) over a specified interval,

and estimates the rate of

change from a graph.




(presented symbolically or as

a table) over a specified

interval.




(presented as a table) over a

specified interval.

Building Functions

A-SSE.4-2

F-BF.1b-1

F-BF.2

Builds functions that model


situations, including those

requiring trigonometric

functions, sequences and

combinations of these and

other functions, and uses the

models to solve, interpret and

generalize about problems.



situations, including those

requiring trigonometric

functions, sequences and

combinations of these and

other functions, and uses the

models to solve and interpret

problems.



situations, limited to those

requiring arithmetic and

geometric sequences, and

uses the models to solve and

interpret problems.

Identifies functions that model


situations, limited to those

requiring arithmetic and

geometric sequences.






Expectations


Statistics & Probability

S-IC.3-1

Determines why a sample survey,

experiment or observational

study is most appropriate.

Given an inappropriate choice

of a sample survey,


study, identifies and supports

the appropriate choice.

Determines how to change the

scenario to make the choice

appropriate.

Determines whether a sample

survey, experiment or

observational study is most

appropriate.

Identifies whether a given

scenario represents a sample


observational study.

Identifies characteristics of a

sample survey, experiment or




Algebra II: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with

connections to the Standards for Mathematical Practice.



Expectations


F-IF.7c F-IF.7e-1 F-IF.7e-2 F-IF.8b F-IF.9-2 F-Int.1-2

Given multiple functions in

different forms (algebraically,

graphically, numerically and by

verbal description), writes

multiple equivalent versions of

the functions, and identifies

and compares key features.

Graphs exponential,

polynomial, trigonometric,

and logarithmic functions,


Given functions represented

algebraically, graphically,

numerically and by verbal

description, writes multiple

equivalent versions of the

functions and identifies key

features.

Graphs exponential and

polynomial functions, showing

key features.




description, writes equivalent

versions of the functions, and


Graphs polynomial


features.

Given functions represented algebraically, graphically, numerically and by verbal description, identifies key features of the functions.


N-CN.1 N-CN.2 A-APR.6

Uses commutative,

associative and distributive

properties to perform

operations with complex

numbers.

Rewrites simple rational

expressions using inspection or

long division.

Uses commutative, associative

and distributive properties to

perform operations with

complex numbers.


expressions using inspection.

Uses commutative and

associative properties to add

and subtract complex

numbers and multiply a

complex number by a real

number.

Uses commutative and associative properties to add and subtract complex numbers.







Expectations


F-BF.3-2 F-BF.3-3 F-BF.3-5



graphs of polynomial,

exponential, logarithmic and

trigonometric functions, and

determines if the resulting

function is even or odd.




logarithmic and trigonometric

function - including f(x)+k,

kf(x), f(kx), and f(x+k) – and







trigonometric functions -

limited to f(x)+k and kf(x) -

and determines if the

resulting function is even or

odd.

Identifies the effects of a single transformation on graphs of polynomial and exponential functions - limited to f(x)+k.

Trigonometry

F-TF.1 F-TF.8-2

Given a trigonometric value and quadrant for an angle, utilizes the structure and relationships of trigonometry, including relationships in the unit circle, to identify other trigonometric values for that angle, and describes the relationship between the radian measure and the subtended arc in the circle.

Given a trigonometric value

and quadrant for an angle,

utilizes the structure and

relationships of trigonometry,

including relationships in the

unit circle, to identify other

trigonometric values for that

angle.




relationships of trigonometry

to identify other trigonometric

values for that angle.

Given a trigonometric value for an angle in quadrant 1, utilizes the structure and relationships of trigonometry to identify other trigonometric values for that angle.







Expectations

Solving Equations

and Systems N-CN.7 A-REI.4b-2 A-REI.6-2 A-REI.7 F-Int.3 F-BF.Int.2 F-LE.2-3 HS-Int.3-3

Solves multi-step contextual

word problems involving

linear, exponential, quadratic

(with real or complex

solutions) and trigonometric

equations and systems of

equations, using inverses

where appropriate.

Constructs linear and

exponential function models

in multi‐step contextual

problems.

Solves problems involving

linear, exponential, quadratic

(with real or complex

solutions) and trigonometric



where appropriate.


exponential function models in

multi-step contextual

problems with mathematical

prompting.


linear, exponential and

quadratic (with real solutions)



where appropriate.



in multi‐step contextual


prompting.

Solves problems involving linear, exponential and quadratic (with real solutions) equations.

Constructs linear function models in multi-step contextual problems with mathematical prompting.

Data – Univariate and Bivariate

S-ID.4

S-ID.6a-1

S-ID.6a-2

Uses the means and standard

deviations of data sets to fit

them to normal distributions.

Fits exponential and

trigonometric functions to data

in order to solve multi- step

contextual problems. Determines when models fitted

to data are inappropriate.


deviations of data sets to fit them

to normal distributions.

Fits exponential functions to

data in order to solve multi‐

step contextual problems.




Uses fitted exponential

functions to solve multi-step


Identifies the mean and standard

deviation of a given normal

distribution.







Expectations

Inference

S-IC.2 S-IC.Int.1

Uses sample data to make, justify, and critique inferences and conclusions about the corresponding population.

Decides if specified models are

consistent with results from

given data-generating processes.

Uses sample data to make

inferences about the

corresponding population.

Identifies when sample data can be used to make inferences about the corresponding population.

Identifies when sample data can

be used to make inferences

about the corresponding

population.

Probability

S-CP.Int.1

Recognizes, determines and

uses conditional probability and

independence in multi-step

contextual problems, using

appropriate set language and

appropriate representations,

including two-way frequency

tables.

Applies the Addition Rule of

probability.

Recognizes, determines and uses

conditional probability and

independence in contextual

problems, using appropriate set

language and appropriate

representations, including two-

way frequency tables.

Recognizes and determines conditional probability and independence in contextual problems.

Recognizes and determines


problems.



Algebra II: Sub-Claim C In connection with content, the student expresses grade/course-level appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statement.



Expectations

Reasoning HS.C.3.1 HS.C.3.2 HS.C.4.1 HS.C.5.4 HS.C.5.11 HS.C.6.2 HS.C.6.4 HS.C.7.1 HS.C.8.2 HS.C.8.3 HS.C.9.2 HS.C.11.1 HS.C.12.2 HS.C.16.3 HS.C.17.2 HS.C.17.3 HS.C.17.4 HS.C.17.5 HS.C.18.4 HS.C.CCR





communicates a complete

response based on:

a response to a given equation

or system of equations

a chain of reasoning to justify

or refute algebraic, function or

number system propositions or

conjectures

a response based on data

a response based on the graph

of an equation in two variables,

the principle that a graph is a

solution set or the relationship

between zeros and factors of

polynomials

a response based on

trigonometric functions and

the unit circle

a response based on transformations of functions

OR

a response based on properties of exponents

by:

using a logical approach based on a conjecture and/or stated





communicates a response based

on: • a response to a given equation

or system of equations • a chain of reasoning to justify



conjectures, • a response based on data • a response based on the graph

of an equation in two variables,

the principle that a graph is a

solution set or the relationship

between zeros and factors of

polynomials • a response based on


the unit circle • a response based on


OR • a response based on properties

of exponents by:







the student constructs and


based on:






conjectures



of an equation in two

variables, the principle that a

graph is a solution set or the

relationship between zeros

and factors of polynomials

a response based on


the unit circle

a response based on

transformations of functions OR

a response based on properties

of exponents by:







communicates an incomplete

response based on:





number system propositions

or conjectures



of an equation in two

variables, the principle that a

graph is a solution set or the

relationship between zeros

and factors of polynomials

a response based on


the unit circle

a response based on

transformations of functions OR

a response based on

properties of exponents by :

using an approach based

on a conjecture and/or



Algebra II: Sub-Claim C In connection with content, the student expresses grade/course-level appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statement.



Expectations

assumptions, utilizing mathematical connections (when appropriate)

providing an efficient and logical progression of steps or chain of reasoning with appropriate justification

performing precise calculations

using correct grade- level vocabulary, symbols and labels


determining whether an argument or conclusion is generalizable

evaluating, interpreting and critiquing the validity of others’ responses, approaches and reasoning – utilizing mathematical connections (when appropriate) – and providing a counter-example where applicable


(when appropriate)

providing a logical progression

of steps or chain of reasoning

with appropriate justification

performing precise

calculations

using correct grade- level

vocabulary, symbols and

labels


evaluating, interpreting and critiquing the validity of others’ responses, approaches and reasoning – utilizing mathematical connections (when appropriate)

assumptions

providing a logical, but

incomplete, progression of

steps or chain of reasoning

performing minor calculation errors

using some grade-level


labels

providing a partial

justification of a conclusion

based on own calculations

evaluating the validity of

others’ approaches and

conclusions.

stated or faulty

assumptions

providing an incomplete or

illogical progression of steps

or chain of reasoning

making an intrusive

calculation error

using limited grade-level


labels

providing a partial

justification of a

conclusion based on

own calculations



Algebra II: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by

applying knowledge and skills articulated in the standards for the current grade/course (or for more complex problems, knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling practice, and where helpful

making sense of problems and persevering to solve them, reasoning abstractly, and quantitatively, using appropriate tools strategically, looking for the making use of structure and/or looking for and expressing regularity in repeated reasoning


Expectations

Modeling

HS.D.2-4 HS.D.2-7 HS.D.2-10 HS.D.2-13 HS.D.3-5a HS.D.3-6 HS.D.CCR

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, devises a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by:

using stated assumptions and approximations to simplify a real‐world situation

mapping relationship between important quantities

selecting appropriate tools to create the appropriate model

analyzing relationships mathematically between important quantities (either given or created) to draw conclusion


reflecting on whether the

results make sense


writing a complete, clear and correct expression, equation or function to describe a situation

analyzing and/or creating

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, devises a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by: using stated assumptions and

approximations to simplify a real-world situation


selecting appropriate tools to create the appropriate model

analyzing relationships mathematically between important quantities (either given or created) to draw conclusions


reflecting on whether the

results make sense

improving the model if it has

not served its purpose

writing a complete, clear and correct expression, equation or function to describe a situation



illustrating relationships between important quantities

using provided tools to create appropriate but inaccurate model

analyzing relationships mathematically between important given quantities to draw conclusions

interpreting mathematical results in a simplified context


modifying the model if it has not served its purpose

writing an expression, equation or function to describe a situation.

using geometry to solve design



identifying important given quantities

using provided tools to create inaccurate model

analyzing relationships mathematically to draw conclusions

writing an expression, equation or function to describe a situation

using securely held content incompletely reporting a conclusion, with some inaccuracy within the reporting

indiscriminately using data from a data source

using securely held content

incompletely reporting a

conclusion, with some

inaccuracy within the reporting



Algebra II: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by


making sense of problems and persevering to solve them, reasoning abstractly, and quantitatively, using appropriate tools strategically, looking for the making use of structure and/or looking for and expressing regularity in repeated reasoning


Expectations constraints, relationships and goals

justifying and defending models which lead to a conclusion

using geometry to solve design problems

using securely held content, accurately reporting and justifying the conclusion

identifying and using relevant data from a data source

making an appropriate evaluation or recommendation

using geometry to solve design problems

using securely held content, briefly, but accurately reporting the conclusion

identifying and using relevant data from a data source

making an appropriate evaluation or recommendation

problems

using securely held content, incompletely reporting a conclusion

selecting and using some relevant data from a data source

making an evaluation or recommendation

indiscriminately using data from

a data source

Performance Level Descriptors – Integrated Mathematics I


Math I: Sub-Claim A The student solves problems involving the Major Content for the grade/course with connections to the Standards for



Expectations


Expressions and Equations

A.SSE.1-1

A.Int.1

A.CED.4-1

A.REI.3

A.SSE.3c-1

A.SSE.3c-2

Manipulates linear formulas

and equations to highlight a

quantity of interest in context.

Interprets components of

contextual exponential

expressions and solves

equations that require seeing

structure.


and equations for a specified

variable.

Identifies components of


expressions and solves

equations that require

seeing structure.


and equations to solve for a

specified variable requiring

one step.

Identifies components of


expressions.


and equations to solve for a

specified variable requiring

one step.

Rate of Change

F.IF.6-3a

F.IF.6-3b F.IF.6-8



linear, exponential, square

root, cube root and

piecewise-defined functions



interval, and estimates the

rate of change from a graph.



intervals.


change of linear and


(presented symbolically or as a

table) over a specified interval

and estimate the rate of

change from a graph.






interval.




(presented as a table) over a

specified interval.






Expectations



F.BF.2

F.Int.1-3

F.IF.1

F.IF.2

F.IF.A.Int.1

F.IF.4-3 F.IF.5-1 S.ID.Int.1 HS.Int.3-1

Determines if a given relation

is a function.

Evaluates with, uses and

interprets with function

notation within a context.

Writes and uses arithmetic and

geometric sequences to model

situations.

For linear functions that model

contextual relationships,

determines and interprets key

features, graphs the function

and solves problems.

Determines the domain and

relates it to the quantitative

relationship it describes for a

linear, exponential (limited to

domains in the integers),

square root, cube root,

piecewise, step and absolute

value functions.


is a function.


function notation within a

context.

Writes arithmetic and

geometric sequences.

For linear functions that model


determines key features and

graphs the function.

Determines the domain and

relates it to the quantitative

relationship it describes for

linear and exponential

(limited to domains in the

integers) functions.


is a function.


function notation.

Writes arithmetic sequences.

For linear functions that

model contextual


features.

Determines the domain of

linear functions.

Determines if a given relation is a function. Evaluates with and uses

function notation.

Identifies arithmetic

sequences.

Given the graph of linear

functions that model


determines key features.






Expectations


Solving Graphically

A.REI.10

A.REI.11-1a

A.REI.11-1b A.REI.12 A.CED.3-1

Graphs and analyzes the

solution sets of equations,

linear inequalities and

systems of linear inequalities.







approximations.

Writes a system of linear

inequalities given a context.



and systems of linear


inequalities.







approximations.

Graphs the solution sets of equations and linear inequalities







approximations.

Graphs the solution sets of equations and inequalities.

Given the graph, finds the solutions to a system of two polynomial functions.

Congruence Transformations

G.CO.C G.CO.6

Determines and uses

appropriate geometric



triangles and parallelograms

to solve problems and prove




congruence.




triangles and parallelograms

to solve routine problems and

prove statements about

angle measurement,

triangles, distance, line

properties and congruence.

Uses given geometric theorems and properties of rigid motions, lines, angles, triangles and parallelograms to solve routine problems and reason about angle measurement, triangles, distance, line properties and congruence.

Uses given geometric theorems and properties of rigid motions, lines, angles, triangles and parallelograms to solve routine problems.



Math I: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with connections to the



Expectations


Summarizing, Representing and Interpreting Data

S.ID.5

Determines appropriate representations of categorical and quantitative data, summarizing and interpreting the data and characteristics of the representations.

Describes and interprets possible associations and trends in the data.

Determines appropriate representations of categorical quantitative data, summarizing the data and characteristics of the representations.

Given representations of categorical and quantitative data, summarizes the data and characteristics of the representations.

Given representations of categorical and quantitative data, describes characteristics of the data representations.

Transformations

G.CO.1

G.CO.3 G.CO.5

Given a figure and a transformation (or a sequence of transformations), draws the transformed figure.

Uses precise geometric terminology to specify a sequence of transformations that will carry a figure onto itself or another.

Given a figure and transformation, draws the transformed figure. Specifies a sequence of transformations that will carry a figure onto another.

Given a figure and a transformation, draws the transformed figure.

Given a figure and a transformation, identifies the transformed figure.

Solving Systems

A.REI.6-1 A.REI.6-2

Solves multi-step contextual problems that require writing, solving and analyzing systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables with real coefficients and solutions. Solves a given system of three linear equations and three unknowns with rational coefficients.

Given a system of linear equations, solves contextual problems exactly and approximately, focusing on pairs of linear equations in two variables with rational coefficients and solutions.

Given a system of linear equations, solves contextual problems exactly and approximately, focusing on pairs of linear equations in two variables with integer coefficients and solutions.

Given the graph of a system of linear equations, identifies the solution to contextual problems exactly and approximately, focusing on pairs of linear equations in two variables with integer coefficients and solutions.



Math I: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with connections to the



Expectations


Contextual Problems Functions

F.IF.7a-1

F.IF.9-3

F.LE.2-1

F.LE.2-2 F.LE.2-3

Represents linear and exponential (with domain in the integers) functions symbolically, in real-life scenarios, graphically, with a verbal description, as a sequence and with input‐ output pairs to solve mathematical and contextual problems.

Compares the properties of two functions represented in multiple ways, limited to linear, exponential (with domains in the integers), square root, cube root, piece-wise, step and absolute value.

Represents linear and exponential (with domain in the integers) functions symbolically, graphically and with input-output pairs to solve mathematical problems.

Compares the properties of two functions represented in different ways, limited to linear and exponential (with domains in the integers).

Given a symbolic representation, real-life scenario, graph, verbal description, sequence or input-output pairs for linear and exponential functions (with domains in the integers), solves mathematical problems.

Compares the properties of two linear functions represented in different ways.

Given a symbolic representation, real-life scenario, graph, verbal description, sequence or input-output pairs for linear functions, solves mathematical problems. Compares the properties of two linear functions represented in different ways.



Math I: Sub-Claim C In connection with content, the student expresses grade/course-level appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statements.


Expectations


Reasoning

HS.C.5.6 HS.C.5.10-2 HS.C.6.1 HS.C.10.1 HS.C.14.1 HS.C.14.2 HS.C.18.1



described in Sub-claims A and

B, the student clearly

constructs and communicates

a complete response based

on: • the principle that a graph of

an equation in two variables

is the set of all its solutions • reasoning about linear and

exponential growth

• properties of rational

numbers or irrational

numbers • transformations of functions • a chain of reasoning to justify

or refute algebraic, function,

or linear equation

propositions or conjectures • a given equation or system of

equations • the number or nature of

solutions by: • using a logical approach based

on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)

• providing an efficient and logical progression of steps or chain of reasoning with appropriate justification




B, the student clearly

constructs and communicates

a response based on: • the principle that a graph of



exponential growth

• properties of rational


numbers

• transformations of functions • a chain of reasoning to justify


or linear equation



solutions by: • using a logical approach

based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)

• providing a logical progression of steps or chain of reasoning with appropriate justification






based on: • the principle that a graph of an

equation in two variables is

the set of all its solutions • reasoning about linear and

exponential growth

• properties of rational numbers

or irrational numbers • transformations of functions • a chain of reasoning to justify


or linear equation propositions

or conjectures • a given equation or system of


solutions by:

• using a logical approach based on a conjecture and/or stated assumptions

• providing a logical, but incomplete, progression of steps or chain of reasoning

• performing minor calculation errors

• using some grade-level vocabulary, symbols and labels






response based on: • the principle that a graph of



exponential growth • properties of rational


numbers



or linear equation



solutions by: • using an approach based on

a conjecture and/or stated or faulty assumptions

• providing an incomplete or illogical progression of steps or chain of reasoning

• making an intrusive calculation error

• using limited grade-level vocabulary, symbols and



Math I: Sub-Claim C In connection with content, the student expresses grade/course-level appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statements.


Expectations


• performing precise calculations

• using correct grade-level vocabulary, symbols and labels

• providing a justification of a conclusion

• determining whether an argument or conclusion is generalizable

• evaluating, interpreting and critiquing the validity of others’ responses, approaches and reasoning – utilizing mathematical connections (when appropriate) and providing a counter-example where applicable.




• evaluating, interpreting and critiquing the validity of others’ responses, approaches and reasoning – utilizing mathematical connections (when appropriate).

• providing a partial justification of a conclusion based on own calculations

• evaluating the validity of others’ approaches and conclusions.

labels • providing a partial

justification of a conclusion based on own calculations.



Math I: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by


making sense of problems and persevering to solve them, reasoning abstractly, and quantitatively, using appropriate tools strategically, looking for the making use of structure and/or looking for and expressing regularity in repeated reasoning.



Expectations

Modeling

HS.D.1-1 HS.D.2-5 HS.D.2-8 HS.D.3-1b HS.D.3-3b

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, devises and enacts a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by: • using stated assumptions and

making assumptions and approximations to simplify a real-world situation (includes micro-models)

• mapping relationships between important quantities


• analyzing relationships mathematically between important quantities to draw conclusion

• analyzing and/or creating constraints, relationships and goals

• interpreting mathematical results in the context of the situation

• reflecting on whether the results make sense

• improving the model if it has not served its purpose

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, devises and enacts a plan to apply mathematics in solving problems arising I everyday life, society and the workplace by: • using stated assumptions and




• analyzing relationships



conclusions





served its purpose • writing a complete, clear and

correct algebraic expression or

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, devises and enacts a plan to apply mathematics in solving problems arising in everyday life, society and the

workplace by: • using stated assumptions and


• illustrating relationships between important quantities

• using provided tools to create models



in a simplified context • reflecting on whether the results

make sense

• modifying the model if it has not

served its purpose • writing an algebraic expression

or equation to describe a situation

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, devises a plan to apply mathematics in solving problems arising in everyday life, society and the



• identifying important quantities


• analyzing relationships mathematically to draw conclusions

• writing an algebraic expression or equation to describe a situation

• applying proportional reasoning and percentages

• applying common geometric principles and theorems

• using functions to describe how one quantity of interest



Math I: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by


making sense of problems and persevering to solve them, reasoning abstractly, and quantitatively, using appropriate tools strategically, looking for the making use of structure and/or looking for and expressing regularity in repeated reasoning.



Expectations

• writing a complete, clear and correct algebraic expression or equation to describe a situation

• applying proportional reasoning and percentages justifying and defending models which lead to a conclusion

• applying geometric principals and theorems


• using statistics


equation to describe a situation • applying proportional reasoning

and percentages • applying geometric principles and

theorems • writing and using functions in any

form to describe how one quantity of interest depends on another




• applying geometric principles and theorems

• writing and using functions to describe how one quantity of interest depends on another

• using statistics • using reasonable estimates of

known quantities in a chain of reasoning that yields an estimate of an unknown quantity

depends on another • using statistics • using estimates of known


Performance Level Descriptors – Integrated Mathematics II


Math II: Sub-Claim A The student solves problems involving the Major Content for the grade/course with connections to the Standards for




Expectations

Quadratics and Exponential

Expressions

A.SSE.1-2

A.SSE.2-2

A.SSE.2-5

A.SSE.3a

A.SSE.3b

Interprets the structure of equivalent quadratic and exponential expression that contain real exponents.

Writes equivalent expressions

to reveal information by

viewing one or more of their

parts as a single entity,

including factoring and

completing the square for

quadratics.

Interprets the structure of

equivalent quadratic and

exponential expressions (with

rational exponents) to reveal

information by viewing at

least one of their parts as a

single entity.

Identifies equivalent quadratic and exponential expressions with integer exponents.

Identifies equivalent exponential expressions with integer exponents.

Quadratic Equations

A.REI.4a-1 A.REI.4b-1

A.REI.4b-2 A.CED.4-2 HS.Int.2

Solves quadratic equations in one variable with real coefficients, using methods appropriate to the initial form, including completing the square, inspection, taking square roots, the quadratic formula and factoring. Recognizes when the quadratic formula give complex solutions.

Solves quadratic equation in

one variable with rational

coefficients, using method

including completing the

square, inspection, taking

square roots, the quadratic

formula or factoring.

Identifies solutions to quadratic equations in one variable with integer or rational coefficients.

Identifies solutions to quadratic equations in one variable with integer coefficients.







Expectations

Graphing Exponential and Quadratic Functions

F.IF.4-4 F.IF.5-2 HS.Int-1

Writes quadratic and

exponential functions,

determines key features,

graphs functions and solves

problems in contextual

situations.

Determines domains and relates them to the quantitative relationship described for quadratic functions.

For quadratic and

exponential functions that

model contextual

relationships, determines

key features and sketches

graphs of functions.

Determines domains of

quadratic functions.

Identifies key features of quadratic and exponential functions.

Given a graph, identifies key features of quadratic and exponential functions.

Rate of Change

F.IF.6-4 F.IF.6-9



exponential and quadratic




rate of change from a graph. Compares rates of change


intervals.


change of exponential and

quadratic functions



interval and estimate the


Calculates the average rate of change of exponential and quadratic functions (presented symbolically or as a table) over a specified interval.

Calculates the average rate of change of exponential and quadratic functions (presented as a table) over a specified interval.

Polynomial, Rational and

Radical Expressions N.RN.2 A.APR.1-1

Adds, subtracts and multiplies three or more polynomials. Using the properties of exponents, rewrites expressions containing radicals and rational exponents.

Adds, subtracts and multiplies two polynomials. Using the properties of

exponents, rewrites

expressions containing

rational exponents.

Identifies equivalent expressions when adding, subtracting and multiplying polynomials and expressions containing integer exponents.

Identifies equivalent expressions when adding and subtracting polynomials and expressions containing integer exponents.







Expectations

Similarity

G.SRT.1a G.SRT.1b G.SRT.2 G.SRT.5

Uses transformations and

congruence and similarity

criteria for triangles to

prove relationships among

geometric figures and to

solve problems.

Uses transformations to determine relationships among simple geometric figures and to solve problems.

Identifies transformation relationships in simple geometric figures.

Identifies transformation relationships in simple geometric figures in cases where an image is provided.

Similarity in Trigonometry

G.SRT.6 G.SRT.7-2 G.SRT.8






Uses similarity

transformations with right

triangles to define

trigonometric ratios for acute

angles.

Uses trigonometric ratios, the Pythagorean Theorem and the relationship between sine and cosine to solve right triangles in applied problems.

Uses trigonometric ratios and the Pythagorean Theorem to determine the unknown side lengths and angle measurements of a right triangle.

Uses trigonometric ratios and the Pythagorean Theorem to determine the unknown side lengths of a right triangle.



Math II: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with connections to the




Expectations

Probability

S.CP.Int.1


uses conditional probability and

independence in multi- step


appropriate set language and

appropriate representations,

including two-way frequency

tables.

Applies the Addition Rule

of probability.


uses conditional probability

and independence in


appropriate set language

and appropriate

representations, including

two-way frequency tables.


conditional probability and


problems.



problems.

Statistics

S.ID.6a-1 S.ID.Int.2

Represents data on scatter

plots and describes how the

variables are related.

Fits quadratic functions to

data to solve problems in the

context of the data and

informally assesses the fit of

functions by plotting and

analyzing residuals.

Represents data on scatter plots

and describes how the

variables are related.

Informally, determines

whether quadratic models

are a good fit.

Fits quadratic functions to

data to solve problems in

the context of the data.


plots.

Informally, determines whether quadratic models are a good fit. Uses fitted quadratic functions to solve contextual problems.


plots.

Informally, determines

whether quadratic models are

a good fit.







Expectations

Geometric Formulas

G.GMD.1 G.GMD.3

Uses volume formulas to solve


problems that involve

cylinders, pyramids, cones and

spheres.

Uses dissection arguments,

Cavalieri’s principle and

informal limit arguments to

support the formula for the

circumference of a circle, area

of a circle, volume of a

cylinder, pyramid, and cone.

Using formulas, determines

the volume of cylinders,

pyramids, cones and spheres.

Gives an informal argument for

the formula for the

circumference of a circle and

area of a circle, including

dissection arguments.

Using formulas, determines

the volume of cylinders,

pyramids, cones and spheres.

Using formulas, determines the

volume of cylinders, pyramids,

cones and spheres.

Graphs

F.IF.7a-2

F.IF.7b

F.IF.7e-1

F.BF.3-1 F.BF.3-4 HS-Int.2

Graphs and compares

exponential, quadratic, square

root, cube root, piece-wise-

defined functions (including

step functions and absolute

value functions), identifying

intercepts, maxima and

minima, end behavior and

zeros.

Identifies and illustrates the

effect on linear and quadratic

graphs of replacing f(x) by

f(x)+k, kf(x), f(kx), and f(x+k) for

specific values of k. Finds the

values of k given the graphs.

Graphs exponential and

quadratic functions,

identifying intercepts, maxima

and minima, end behavior and

zeros.

Identifies and illustrates the

effect on linear and quadratic

graphs of replacing f(x) by one

of the following: f(x)+k, kf(x),

f(kx), and f(x+k) for specific

values of k. Finds the values of

k given the graphs.

Identifies intercepts, maxima

and minima, end behavior

and zeros from graphs

Identifies the effect on linear

and quadratic graphs of

replacing f(x) by one of the

following f(x)+k, kf(x), f(kx),

and f(x+k) for specific values

of k.

Identifies intercepts, maxima

and minima and zeros from

graphs.

Identifies the effect on linear

and quadratic graphs of

replacing f(x) by f(x)+k for

specific values of k.







Expectations

Multiple Representations of Functions

A.REI.7

F.Int.1-4

F.BF.1b-1 F.IF.8a F.IF.8b F.IF.9-4 HS.Int.1

Writes quadratic or

exponential functions defined

by expressions in different but

equivalent forms to reveal

and explain different

properties of the functions,

including zeros, extreme

values, symmetry and percent

rate of change.

Within a context, compares

properties of two functions

represented in different ways

(algebraically, graphically,

numerically or verbally).

Solves a simple system of

linear and quadratic

equations algebraically or

graphically.

Combines standard functions

using arithmetic operations.

Writes quadratic or

exponential functions defined

by expressions in different

but equivalent forms to

reveal and explain different

properties of the functions,


values, symmetry and percent

rate of change.

Within a routine context,

compares properties of two

functions represented in

different ways (algebraically,

graphically, numerically or

verbally).

Given a graph, solves a

system of a linear and

quadratic equations.

Given equivalent expressions,

identifies features of

quadratic or exponential

functions, including zeros,

extreme values and percent

rate of change.

Compares properties of two

functions within the same

representation.

Given equivalent expressions,

identifies features of

exponential functions,


values and percent rate of

change.







Expectations

Number Systems

N.RN.B-1

N.CN.1

N.CN.2 N.CN.7

Identifies rational, irrational

and complex numbers.

Uses commutative,



operations with complex

numbers.

Calculates sums and products

of two rational and/or

irrational numbers and

determines whether and

generalizes when the sums

and products are rational or

irrational.



Uses commutative,



operation with complex

numbers.

Calculates sums and products

of two rational and/or

irrational numbers.



Uses commutative and



numbers and to multiply a

complex number by a real

number.


and complex numbers. Uses commutative and



numbers.



Math II: Sub-Claim C In connection with content, the student expresses grade/course-level appropriate mathematical reasoning by constructing viable

arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statements



Expectations

Reasoning

HS.C.2.1 HS.C.3.1 HS.C.3.2 HS.C.5.5 HS.C.8.1 HS.C.9.1 HS.C.12.1 HS.C.12.2 HS.C.14.5 HS.C.14.6 HS.C.15.14 HS.C.16.2 HS.C.18.3




the student clearly constructs and

communicates a complete

response based on:

• the principle that the graph of an

equation in two variables is the set of all its solutions

• reasoning about linear and exponential growth

• properties of rational numbers or irrational numbers

• transformations of functions

• a chain of reasoning to justify or refute algebraic, function- related, or linear equation propositions or conjectures

• a given equation or system of equations

by:

• using a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)

• providing an efficient and logical progression of steps or chain of reasoning with appropriate justification





communicates a response based

on:

• the principle that the graph of

an equation in two variables is the set of all its solutions






by:

• using a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)





B, the student constructs and

communicates a partial

response based on:

• the principle that the graph of

an equation in two variables is the set of all its solutions





• a given equation or system of equations by:

• using a logical approach based on a conjecture and/or stated assumptions

• providing a logical, but incomplete, progression of steps or chain of reasoning






response based on:

• the principle that the graph of an equation in two variables is the set of all its solutions




or refute algebraic, function- related, or linear equation propositions or conjectures


by:

• using an approach based on a conjecture and/or stated or faulty assumptions


• making an intrusive



Math II: Sub-Claim C In connection with content, the student expresses grade/course-level appropriate mathematical reasoning by constructing viable

arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statements



Expectations

• performing precise calculations • using correct grade- level


conclusion • determining whether an

argument or conclusion is generalizable.

• evaluating, interpreting and critiquing the validity of others’ responses, approaches and reasoning – utilizing mathematical connections (when appropriate) – and providing a counter-example where applicable




• evaluating, interpreting and critiquing the validity of others’ responses, approaches and reasoning – utilizing mathematical connections (when appropriate).

• performing minor calculation errors

• using some grade-level vocabulary, symbols and labels


• evaluating the validity of others’ approaches and conclusions

calculation error • using limited grade-level





Math II: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by





Expectations

Modeling

HS.D.1-2 HS.D.2-1 HS.D.2-2 HS.D.2-6 HS.D.2-9 HS.D.2-11 HS.D.3-2b HS.D.3-4b






arising in everyday life, society and the





• analyzing relationships mathematically between important quantities to draw conclusion





served its purpose • writing a complete, clear and










• selecting appropriate tools to create models • analyzing relationships

mathematically between important quantities to draw conclusions








devises and enacts a plan to

apply mathematics in solving

problems arising in everyday life,

society and the workplace by: • using stated assumptions

and approximations to simplify a real-world situation




• interpreting mathematical results in a simplified context


• modifying the model if it has not served its purpose

• writing an algebraic expression or equation to




devises a plan to apply


arising in everyday life, society

and the workplace by: • using stated assumptions and


• identifying important quantities


• analyzing relationships mathematically to draw conclusions

• writing an algebraic expression or equation to describe a situation


reasoning and percentages

• applying common geometric principles and theorems

• using functions to describe how one quantity of interest



Math II: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by





Expectations correct algebraic expression or equation to describe a situation

• applying proportional reasoning and percentages justifying and defending models which lead to a conclusion

• applying geometric principles and theorems



using reasonable estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity.

correct algebraic expression or equation to describe a situation


• applying geometric principles

and theorems • writing and using functions in

any form to describe how one quantity of interest depends on another


known quantities in a chain of reasoning that yields an estimate of an unknown quantity.

describe a situation • applying proportional

reasoning and percentages • applying geometric principles

and theorems • writing and using functions

to describe how one quantity of interest depends on another


known quantities in a chain of reasoning that yields an estimate of an unknown quantity.

depends on another

• using basic statistics

• using estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity.

Performance Level Descriptors – Integrated Mathematics III


Math III: Sub-Claim A The student solves problems involving the Major Content for the grade/course with connections to the Standards for




Expectations


A-SSE.2-3

A-SSE.2-6

Uses the structure of

polynomial, exponential and

rational expressions to create

equivalent expressions that

aid in solving mathematical

problems.


polynomial, exponential and

rational expressions to create







exponential expressions to

create equivalent expressions.


A-APR.2

A-APR.3-1

F-IF.4-5


and relationships to reveal key


rational, trigonometric and

logarithmic functions to sketch

graphs and identify


relationship between two

quantities.

Identifies zeros and sketches

graphs of quadratics and

cubics, applying the

remainder theorem where

appropriate.

Interprets key features of

graphs and tables, and uses

mathematical properties and

relationships to reveal key

features of polynomial and

rational functions to sketch

graphs. Identifies zeros and sketches

graphs of easily factorable

quadratics and cubics.

Uses provided

mathematical properties

and relationships to reveal

key features of polynomial

functions to sketch graphs.

Identifies zeros of easily

factorable quadratics and

cubics.

Given a graph of a polynomial function, identifies key features. Identifies zeros of easily

factorable quadratics.

Rate of Change

F-IF.6-5 F-IF.6-10



polynomial, logarithmic or

trigonometric functions







change of polynomial


symbolically or as a table) over

a specified interval, and

estimates the rate of change

from a graph.


change of polynomial


symbolically or as a table)

over a specified interval.


change of polynomial functions

(presented as a graph or table)

over a specified interval.







Expectations


intervals.

Solving Equations

A-SSE.4-2

A-REI.2

A-REI.11-2 A.Int.1

Solves mathematical

equations directly and

indirectly using structure,

technology, graphs, formulas,

tables of values and

successive approximations,

and gives examples of how

extraneous solutions may

arise.

Solves mathematical equations

directly and indirectly using

structure, technology, graphs,

formulas, tables of values and

successive approximations,

and identifies extraneous

solutions.

Solves mathematical

equations directly and

indirectly using structure,

technology, graphs, formulas,

tables of values and

successive approximations.

Solves mathematical equations

directly using technology,

graphs, formulas, tables of

values and successive

approximations.

Modeling with Geometry

G-GPE.6 G-Int.1





lengths.

Applies geometric concepts

and trigonometric ratios to


applied problems (including

design problems) related to

the Pythagorean theorem,

density, geometric shapes,

their measures and

properties.





lengths.








relationships and the coordinate



Applies geometric concepts

to describe, model and solve






relationships and the coordinate














Expectations

Statistics & Probability

S-IC.3-1

Determines why a sample



appropriate.

Given an inappropriate

choice of a sample survey,


study, identifies and

supports the appropriate

choice, and determines how

to change the scenario to

make the choice

appropriate.

Determines whether a



appropriate.

Identifies whether a given

scenario represents a sample



Identifies characteristics of a





Math III: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with connections to the




Expectations


F-IF.7c

F-IF.7e-2

F-IF.9-5

F-Int.1-5

Given multiple functions in

different forms (algebraically,

graphically, numerically and by

verbal description), writes

multiple equivalent versions of

the functions, and identifies

and compares key features.

Graphs polynomial


logarithmic functions,





description, writes multiple

equivalent versions of the

functions and identifies key

features.

Graphs polynomial functions,





description, writes equivalent

versions of the functions, and


Graphs polynomial functions,





description, identifies key

features.

Expressions and Equations

A-APR.6

F-Int.3

F-BF.Int.2 HS.Int.3-3

Solves multi-step contextual

word problems involving

polynomial and

trigonometric equations,

using inverses where

appropriate.

Constructs linear, quadratic and

exponential function models in

multi-step contextual problems.

Rewrites simple rational expressions using inspection or long division.


polynomial and trigonometric


where appropriate.

Constructs linear, quadratic

and exponential function

models in multi-step

contextual problems with

mathematical prompting.


expressions using inspection.


polynomial equations, using

inverses where appropriate.



in multi-step contextual


prompting.

Solves problems involving polynomial equations.

Constructs linear function

models in multi-step

contextual problems with

mathematical prompting.







Expectations


F-BF.3-2

F-BF.3-3 F-BF.3-5








(Identical to Original Level 4)





trigonometric functions – including f(x)+k, kf(x), f(kx), and f(x+k), and






logarithmic and trigonometric

functions limited to f(x)+k and

kf(x), and determines if the

resulting function is even or

odd.



graphs of polynomial and

exponential functions limited

to f(x)+k.

Trigonometry

F-TF.1 F-TF.8-2

Given a trigonometric value and quadrant for an angle, utilizes the structure and relationships of trigonometry, including relationships in the unit circle, to identify other trigonometric values for that angle, and describes the relationship between the radian measure and the subtended arc in the circle.




relationships of trigonometry,

including relationships in the

unit circle, to identify other

trigonometric values for that

angle.

Given a trigonometric value and

quadrant for an angle, utilizes

the structure and relationships

of trigonometry to identify

other trigonometric values for

that angle.


for an angle in quadrant 1,


relationships of trigonometry

to identify other trigonometric

values for that angle.

Data – Univariate and Bivariate

S-ID.4

S-ID.6a-2




Fits trigonometric functions to

data in order to solve multi-step

contextual problem. Determines when models fitted to data are inappropriate.




Uses fitted trigonometric

functions to solve a multi-

step contextual problem.




Identify the mean and

standard deviation for a given

normal distribution.







Expectations

Inference

S-IC.2 S-IC.Int.1

Uses sample data to make,

justify and critique inferences

and conclusions about the


Decides if specified models

are consistent with results

from given data-generating

processes.

Uses sample data to make



Identifies when sample data can

be used to make inferences

about the corresponding

population.

Identifies when sample data

can be used to make



Properties and Theorems

G-C.2

G-C.B

G-GPE.1-1

G-GPE.1-2 G-GMD.4




problems and model

relationships.


the center and radius of a circle

given by an equation.

Identifies the shapes of two-dimensional cross-sections of three-dimensional objects and identifies three-dimensional objects generated by rotations of two-dimensional objects.




problems. Completes the square to find



Identifies the shapes of two-



Applies properties and theorems of angles, segments and arcs in circles to solve problems.

Identifies the shapes of two‐



Applies provided properties and theorems of angles and segments to solve problems. Identifies the shapes of two‐


three-dimensional objects

when the cross-section is

parallel or perpendicular to

the base.







Expectations

Geometric Constructions

G-CO.D

Makes geometric constructions: copying a segment, copying an angle, bisecting an angle, bisecting a segment, including the perpendicular bisector of a line segment. Given a line and a point not on the line, uses a variety of tools and methods to construct perpendicular and parallel lines, equilateral triangles, squares and regular hexagons inscribed in circles.

Makes geometric constructions: copying a segment, copying an angle, bisecting an angle, bisecting a segment, including the perpendicular bisector of a line segment. Given a line and a point not on

the line, constructs

perpendicular and parallel

lines.

Makes basic geometric constructions: copying a segment, copying an angle, bisecting an angle, bisecting a segment, including the perpendicular bisector of a line segment.

Makes basic geometric constructions: copying a segment, copying an angle.



Math III: Sub-Claim C In connection with content, the student expresses grade/course-level appropriate mathematical reasoning by constructing viable

arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statements.



Expectations

Reasoning

HS.C.4.1 HS.C.5.4 HS.C.5.11 HS.C.6.2 HS.C.6.4 HS.C.7.1 HS.C.8.2 HS.C.8.3 HS.C.9.2 HS.C.11.1 HS.C.13.1 HS.C.13.2 HS.C.13.3 HS.C.14.3 HS.C.16.3 HS.C.17.2 HS.C.17.3 HS.C.17.4 HS.C.17.5 HS.C.18.4 HS.C.CCR

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student clearly constructs and communicates a complete response based on: • a given equation or system of

equations • a chain of reasoning to justify

or refute algebraic, function, or number system related propositions or conjectures,

• data • the graph of an equation in two

variables, the principle that a graph is a solution set or the relationship between zeros and factors of polynomials

• trigonometric functions and the unit circle

• transformations of functions, OR • properties of exponents, by: • using a logical approach based on

a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)

• providing an efficient and logical

progression of steps or chain of reasoning with appropriate justification

• performing precise calculations • using correct grade-level


In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student clearly constructs and communicates a response based on:


• a chain of reasoning to justify or refute algebraic, function, or number system related propositions or conjectures




• transformations of functions, OR • properties of exponents, by: • using a logical approach based on

a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)


• performing precise calculations • using correct grade-level

vocabulary, symbols and labels • providing a justification

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student constructs and communicates a partial response based on: • a given equation or system of

equations • a chain of reasoning to justify

or refute algebraic, function, or number system related propositions or conjectures

• data • the graph of an equation in

two variables, the principle that a graph is a solution set or the relationship between zeros and factors of polynomials


• transformations of functions, OR

• properties of exponents by: • using a logical approach

based on a conjecture and/or stated assumptions

● providing a logical, but

incomplete, progression of steps or chain of reasoning

● performing minor calculation errors

• using some grade-level

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, the student constructs and communicates an incomplete response based on:


• a chain of reasoning to justify or refute algebraic, function, or number system related propositions or conjectures




• transformations of functions, OR

• properties of exponents by : • using an approach based on

a conjecture and/or stated or faulty assumptions


• making an intrusive calculation error

● using limited grade-level vocabulary, symbols and labels



Math III: Sub-Claim C In connection with content, the student expresses grade/course-level appropriate mathematical reasoning by constructing viable

arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statements.



Expectations • providing a justification of a

conclusion • determining whether an

argument or conclusion is generalizable

• evaluating, interpreting and

critiquing the validity of others’ responses, approaches and reasoning – utilizing mathematical connections (when appropriate) – and providing a counter- example where applicable

of a conclusion

evaluating, interpreting and critiquing the validity of others’ responses, approaches and reasoning – utilizing mathematical connections (when appropriate).



• evaluating the validity of

others’ approaches and conclusions

• providing a partial justification

of a conclusion based on own calculations



Math III: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by





Expectations

Modeling

HS.D.2-4 HS.D.2-7 HS.D.2-10 HS.D.2-13 HS.D.3-5b HS.D.3-6 HS.D.CCR


• using stated assumptions and




create the appropriate model • analyzing relationships

mathematically between important quantities (either given or created) to draw conclusions




• writing a complete, clear and correct expression, equation or

In connection with the content knowledge, skills, and abilities described in Sub-claims A and B, devises a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by: • using stated assumptions and




create the appropriate model • analyzing relationships

mathematically between important quantities (either given or created) to draw conclusions








• using provided tools to create appropriate but inaccurate model

• analyzing relationships mathematically between important given quantities to draw conclusions

• interpreting mathematical results in a simplified context


• modifying the model if it has not served its purpose

• writing an expression,



• identifying important given quantities

• using provided tools to create

inaccurate model • analyzing relationships

mathematically to draw conclusions

• writing an expression, equation or function to describe a situation



Math III: Sub-Claim D In connection with content, the student solves real-world problems with a degree of difficulty appropriate to the grade/course by





Expectations function to describe a situation


• justifying and defending models which lead to a conclusion

• using geometry to solve design problems

● using securely held content,

accurately reporting and justifying the conclusion

• identifying and using relevant data

from a data source

making an appropriate evaluation or recommendation.

correct expression, equation or function to describe a situation

• using geometry to solve design

problems

• using securely held content,

briefly, but accurately reporting the conclusion

• identifying and using relevant

data from a data source • making an appropriate evaluation

or recommendation.

equation or function to describe a situation

• using geometry to solve design

problems

• using securely held content, incompletely reporting a conclusion

• selecting and using some

relevant data from a data source

• making an evaluation or recommendation.

• using securely held content,

incompletely reporting a conclusion, with some inaccuracy within the reporting

• indiscriminately using data from a data source.

Performance Level Descriptors Algebra I

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